Simulation of Evacuation Process in a Supermarket with Cellular Automata

Transcription

1 Available online at Procedia Engineering 52 (2013 ) Simulation of Evacuation Process in a Supermarket with Cellular Automata ZHONG Wei a, TU Rui a, YANG Jian-peng b, LIANG Tian-shui a, * a School of Chemical Engineering and Energy, Zhengzhou University, Zhengzhou , China b Nanyang Fire Detachment Fire Bureau of Henan province, Nanyang , China Abstract The evacuation process in a supermarket is simulated by a two-dimensional Cellular Automata (CA) model in this paper. In this model, the interactions among people and those between people and obstacles in forward direction are considered, and the Danger-degree concept is introduced to solve the path select of people evacuation process. This paper studies the effect of different shelves orientation and personal familiarity degree of exits to evacuation time. The result shows if occupants are fewer in supermarket, shelves orientations have little influence on evacuation time; but when occupants are larger, the longitudinal shelves orientation is more appropriate for evacuation in supermarket than transverse shelves orientation. The study also found that the evacuation time reduces, the exits available time improve with the increase of personal familiar with exits by induction. This can provide theoretical foundation for arranging the shelves orientation in supermarket as well as drafting contingency plans of pedestrians induction evacuation The The Authors. Authors. Published Published by Elsevier by Elsevier Ltd. Open access under CC BY-NC-ND license. Ltd. Selection and peer-review under responsibility of School of Engineering of Sun Yat-sen University Keywords: cellular automata; shelves orientation; familiarity degree; supermarket Nomenclature N all neighbourhood cells combination S finite cells status sets W n (x,y) a danger degree of grid X 1 the number of the first group X the total number of occupants Greek symbols familiarity degree a state transition function mapped from S t to S t+1 Subscripts t the present moment 1. Introduction There are dense crowd and heavy fire load in a supermarket, once the supermarket catches a fire, it could cause serious casualties. The supermarket fire occurred in the capital of Paraguay in 2004 caused 504 fatalities. The fire occurred in Dongdu Mansion in Luoyang resulting in 309 fatalities in So it is important to study the peoples evacuation process in supermarket, and reduce the required evacuation time in fire. * Corresponding author. Tel.: ; fax: address: liangtsh@zzu.edu.cn The Authors. Published by Elsevier Ltd. Open access under CC BY-NC-ND license. Selection and peer-review under responsibility of School of Engineering of Sun Yat-sen University doi: /j.proeng

2 688 Zhong Wei et al. / Procedia Engineering 52 ( 2013 ) Many researchers have studied the evacuation process of supermarket in recent years. Zhang Pei-hong analyzed the customers' evacuation behaviors through questionnaire and observations, the results indicate that person s gender and experience affect the evacuation behavior [1]. Zhang Shu-ping investigated peoples evacuation in a large department store, and found out the conversion coefficient of congested in the business hall statistically [2]. Yang Jian-peng et al. study the influence of building exits distribution to evacuation with EVACNET4 [3], and put forward the using rate of unit effective width as the major parameter to evaluate building s evacuation designs. Song Wei-guo et al. simulated the emergency evacuation in a large commercial center with CAFE [4], considering the interactions among pedestrians and those between pedestrians and environment in evacuation process. However, personnel evacuation processes are very complex in a supermarket. The occupants familiarity degrees for exits and the internal layout of supermarket have a significant effect on evacuation process. This paper simulates a supermarket s evacuation process using cellular automata model and analyzes the influence of familiarity degree and shelves orientation to evacuation process quantitatively. 2. Model Introduction 2.1. Cellular Automata Cellular automata (CA), which were introduced by Von Neumann and Ulam in the 1960s, were mainly used for life duplicate functions at beginning. CA is a discrete, decentralized, and spatially extended system consisting of large numbers of simple identical components with local connectivity [5-8]. It saves messy process of constructing differential equation and has a strong ability to express complicated relationship, which becomes a kind of effective dynamic simulation method. In recent years, CA has been widely applied to pedestrian flow, traffic flow and so on. Cell status, neighborhood and update rule are three important components of CA model. The basic rule is that, any cell (i, j) status at t+1 moment is decided by itself and its finite neighborhood cells status at t moment. Namely: S t 1 (S, t ) S is finite cells status sets, N means all neighbourhood cells combination, containing n adjacent cells status space vectors, and is a state transition function mapped from S t to S t Simulation Setting This paper sets the following environment elements: Grid partition: the supermarket plane is divided into rectangular grids uniformly, one grid matches one cell, the size of each cell is 0.4 m 0.4 m; Grid attribute: each grid status may be occupied by wall, shelves, and occupants or be empty at any time. The model established is saved by data file, so that simulation calls it directly next time; Personnel characteristics: occupants are classified by familiarization about exits, regardless of physical condition or age. Evacuees position and characteristics are generated randomly; Time-step: One person can move a grid each time-step. Normally personnel walking speed are 1m/s, therefore evacuation time is 0.4/1=0.4 s for each time-step; Possible movement direction: this paper uses Von Neumann neighborhood. So occupants have four possible movement direction of up, down, left, right, as shown in fig. 1. Fig. 1 Von Neumann neighborhood Fig. 2 Movement rule

3 Zhong Wei et al. / Procedia Engineering 52 ( 2013 ) Danger-Degree Setting According to the distance from an exit, each grid is assigned a fixed value, which is called Danger-degree. Based on three exits respectively defines different risk matrix. Namely: W ( x, y) x i y j (2) n Where, Wn ( x, y) is a danger degree of grid, ( x, y) based on exit n; The value of n is from 1 to 3, grid ( i, j) is the intermediate place coordinate of exit n, its danger degree is 0. In order to ensure occupants can march around when meeting wall or shelves in evacuation process, the danger degree of grid corresponding with internal shelves and around wall need be defined a maximum value, such as After three risk matrixes W 1, W 2, W 3 have been defined respectively, taking the minimum danger degree of cell ( x, y) from three different matrixes and assigning to a new risk matrix, this new risk matrix is called total risk matrix Movement Rule According to the total risk matrix, each circulation begins from the lowest danger degree to the highest. Specific movement rules are shown as follows: Each occupant chooses one cell which has the lowest danger degree from the adjacent four cells at next time-step preferentially, if this cell be occupied at the moment, he or she will consider to turn to other cell unoccupied and lower danger degree; If there are two cells around it have same danger degree, it will prefer to choose a cell unoccupied for moving; If both two cells are not occupied, occupant will move to either cell randomly; If occupant has selected the movement direction cell, it still needs to consider occupy status around the movement direction cell. If entire neighborhood cells around it were occupied, where there is a serious congestion. Because occupants always avoid too close with others [9], the probability of moving to this cell will be decreased, as shown in fig Movement Rule The supermarket modeled in this paper located in the second floor of an actual shopping mall, it is 50 m long and 32 m wide, it has three exits which marked with exit 1 to 3. Exit 1 is the general inlet and outlet, exit 2 and 3 are safety exits which are closed usually. The right of the supermarket has a shopping inlet, a shopping outlet and several checkout counters, as shown in fig. 3. This paper considers two shelves orientations. All shelves are vertical with exit 1 in fig. 3(a), called transverse shelves model; all shelves are parallel with exit 1, as shown in fig. 3(b), called longitudinal shelves model. In order to eliminate the random error caused by personnel distribution in supermarket, conduct five simulations for each case and take the average as the evacuation time. Exit 3 Wall Shopping inlet Shelves Exit 1 Shopping outlet Exit 2 Checkout (a) Transverse shelves model (b) Longitudinal shelves model Fig.3. Supermarket modeled by CA

4 690 Zhong Wei et al. / Procedia Engineering 52 ( 2013 ) Results and Discussion 3.1. Shelves Orientation In order to study the influence of shelves orientations to evacuation process in supermarket, this paper assumes all occupants have same familiarization about three exits. Considering five situations of 200, 400, 600, 800 and 1000 people in supermarket, and the results are shown in fig. 4. Fig. 4(a) shows that if occupants are fewer in supermarket, such as 200 and 400 cases, shelves orientations have little influence on evacuation time; but when occupants are larger, two kinds of shelves orientations have obvious difference. That is because evacuation time is consisting of walking time and bottleneck time. When personnel density is smaller, it will not produce congestion at exits, and evacuation time is mainly decided by walking process. Since the furthest distances from exits are close for two shelves orientations, so there is little difference in evacuation time between two models. Step-length Evacuation time in transverse shelves Congested time in transverse shelves Evacuation time in longitudinal shelves Congested time in longitudinal shelves congestion factor Transverse shelves model Longitudinal shelves model The number of occupants (a) Evacuation time at different occupants The number of occupants (b) Congestion factor at different occupants Fig. 4 the relationship between occupants and evacuation time When personnel density is large, such as 600, 800 and 1000 cases, however, there are serious congestion occur at the shopping inlet and shopping outlet near exit 1. So evacuation time is mainly decided by bottleneck evacuation. Because of the blocking effect of the shelves, the resistance of occupant move to exit 1 in transverse shelves orientation is much less than longitudinal shelves orientation, making personnel density increase rapidly at shopping inlet and shopping outlet. So the congestion in transverse shelves orientation occurs earlier and is more serious than longitudinal shelves orientation. Therefore the longitudinal shelves orientation is more beneficial for evacuation. The congestion factor, defined as the ratio of congested time to total evacuation time, is shown in fig. 4(b). It can be seen that the congestion factor rises gradually with the occupants, and the factor in transverse shelves orientation is higher than longitudinal shelves orientation when the occupants is the same. So it can be concluded that the transverse shelves orientation could lead to a more serious congestion, the arrangement of shelves in the supermarket should use the longitudinal shelves orientation Familiarity Degree In order to study the influence of personal familiarization to evacuation process, occupants are divided into two groups. The first group is familiar with all the exits, and the second group is familiar only with exit 1. The percentage of the first group in total occupants is defined as familiarity degree. Namely: X 1 X (3) Where, is familiarity degree; 1 X is the number of the first group; X is the total number of occupants. All shelves are fixed as transverse orientation, the total number of occupants is 800, and considering five situations of familiarity degree are 0, 0.25, 0.5, 0.75 and 1 respectively. Simulation results as shown in fig. 5:

5 Zhong Wei et al. / Procedia Engineering 52 ( 2013 ) Evacuation step-length Familiarity degree Fig. 5 the relationship of familiarity degree and evacuation time It can be seen in fig. 5. That evacuation time reduce with the increase of familiarity degree. This is due to the number of occupants who choose exit 1 will decrease with the increase of familiarity degree, thus improved congestion at shopping inlet and shopping outlet. This indicates that enhancing personnel familiarity degree can shorten congestion time and improve evacuation efficiency. Fig.6 shows the congested situation at shopping inlet and outlet when the evacuation process complete in exit 2 and 3. When =0, all occupants chose exit 1 to evacuate, so the available time of exit 2 and 3 is 0s; when =0.25, part of occupants select exit 2 and 3 to evacuate, the available time of exit 2 and 3 become 33.6s; when all occupants are familiar with three exits, the available time of exit 2 and 3 is 78.4s. Thus the larger of familiarity degree, the less occupants move to exit 1, the more available time to exit 2 and 3. Fig.7 shows the number of occupants comes out from three exits at different familiarity degree. It can be seen that occupants come out from exit 1 decrease gradually, and occupants come out from exits 2 and 3 increase with the increase of familiarity degree, the difference of occupants evacuate from three exits are small finally, and the congestion in supermarket is improved with the increase of familiarity degree. In the actual evacuation process in supermarket, it is very important to improve the familiarity degree of exits. The manager can induce occupants choose exits not commonly used by fire radio, evacuation signs, indicators and clerks intervention, and the evacuation process could be optimized =0.25, t=33.6s =0.5, t=40s The number of occupants from exit Exit 1 Exit 2 Exit 3 =0.75, t=54.8s =1, t=78.4s Familiarity degree Fig. 6. The utilization of exits at different familiarity degree Fig. 7 the relationship of familiarity degree and evacuation numbers

6 692 Zhong Wei et al. / Procedia Engineering 52 ( 2013 ) Conclusion This paper simulates an actual supermarket with Cellular automata. Studies the influence of different shelves orientation and personal familiarity degree of exits to evacuation time, the results show as follows: If occupants are fewer in supermarket, such as 200 and 400 cases, shelves orientations have little influence on evacuation time; but when occupants are larger, such as 600, 800 and 1000 cases, evacuation time of longitudinal shelves orientation is shorter than transverse shelves orientation ; The ratio of congested time to total evacuation time in transverse shelves orientation is higher than longitudinal shelves orientation when the occupants is the same. That means the transverse shelves orientation is much easier to congestion; The higher of personal familiarity degree with exits, the larger exits utilization, and the smaller evacuation time, as well as improve congestion at shopping inlet and shopping outlet; The number of occupants coming out from exit 1 reduces, the numbers of occupants coming out from exit 2 and 3 increase with the raise of familiarity degree, and converges finally. Acknowledgements This work was supported by National Natural Science Foundation of China (NSFC) under Grant No , and the key technologies research and development program of Henan province under Grant No References [1] P.H. Zhang, R.X. Shang, Z.M. Jiang, Y.H. Liu., Investigation and Analysis of Evacuation Behavior in a Large Shopping Mall, Journal of Northeastern University (Natural Science) 32, p [2] S.P. Zhang, Y.J. Jing, Research of evacuation crowd in the business hall of large department stores, Fire Science and Technology 23, p [3] J.P. Yang, H.P. Zhang, Z. Pan, N. Ma, W.C. Jiang, A Method of Evaluation the Design of Evacuation Based on the Using Rate of Unit Effective Evacuation Width, Engineering Science 8, p. 94. [4] W.G. Song, Y.F. Yu, H.P. Zhang, Evacuation Analysis of a Large Shopping Mall, Engineering Science 7, p. 78. [5] L.Z. Yang, D.L. Zhang, J. Li, W.F. Fang, W.C. Fan, Simulation of evacuation behaviors in fire using special grid, Progress in Natural Science 14, p [6] H.Y. Zeng, The study of Personnel Emergency Evacuation and Simulation Analysis, SCIENCE TECHNOLOGY AND ENGINEERING 30, p [7] S. Zeng, X.Q. Ma, Y.F. Liao, The Research of Evacuation Model in Urban Underground Business Buildings, BUILDING SCIENCE 24, p. 27. [8] C. Burstedde, K. Klauck, A. Schadschneider, J. Zittartz, Simulation of pedestrian dynamics using a two-dimensional cellular automaton, Physical A 295, p [9] Y. Chen, P. Tao, X.Y. Zhang, Computer Simulation Research of Evacuation Property in Super Shopping Mall, COMPUTER TECHNOLOGY AND DEVELOPMENT 20, p. 211.